The image contains two quadratic equations to be solved. The first one is $11x^2 + 9x = -1$, and the second one is $4b^2 - 32 = 8b$.

1. Problem Description

The image contains two quadratic equations to be solved. The first one is $11x^2 + 9x = -1$, and the second one is $4b^2 - 32 = 8b$.

2. Solution Steps

Let's first solve the equation $11x^2 + 9x = -1$.

Step 1: Add 1 to both sides to get a standard quadratic form.

$11x^2 + 9x + 1 = 0$

Step 2: Use the quadratic formula to find the roots.

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 11$, $b = 9$, and $c = 1$.

$x = \frac{-9 \pm \sqrt{9^2 - 4(11)(1)}}{2(11)}$

$x = \frac{-9 \pm \sqrt{81 - 44}}{22}$

$x = \frac{-9 \pm \sqrt{37}}{22}$

Now let's solve the second equation $4b^2 - 32 = 8b$.

Step 1: Subtract $8b$ from both sides to get a standard quadratic form.

$4b^2 - 8b - 32 = 0$

Step 2: Divide the equation by 4 to simplify.

$b^2 - 2b - 8 = 0$

Step 3: Factor the quadratic expression.

$(b - 4)(b + 2) = 0$

Step 4: Set each factor equal to zero and solve for $b$.

$b - 4 = 0 \implies b = 4$

$b + 2 = 0 \implies b = -2$

3. Final Answer

$x = \frac{-9 \pm \sqrt{37}}{22}$

$b = 4, -2$